Image processing device, image processing method, image processing program, and recording medium storing said program

ABSTRACT

An average image producing means  52  produces an average image from all or some of a plurality of images captured at the same location. A noise extracting means  53  extracts a noise pixel on the basis of the result of a comparison between the pixel values of the pixels in the captured images and the pixel values of the pixels at the same position in the average image. An interpolating means  54  interpolates the pixel value of the noise pixel included in the captured images using the pixel values of other pixels to produce a noise-eliminated image.

TECHNICAL FIELD

The present invention relates to an image processing device forprocessing an image obtained by photographing the form of an object suchas an eye to be examined, an image processing method, an imageprocessing program, and a recording medium storing the program.

BACKGROUND ART

Various methods for eliminating noise from images obtained by an imagingdevice such as a CCD have been proposed. For example, Patent Document 1discloses a method in which, on the basis of the pixel value of aselected pixel and the pixel value of a pixel of interest, a new pixelvalue of the pixel of interest is determined, and the pixel value of thepixel of interest is replaced with the new pixel value to generate newimage data, thereby eliminating noise from image data includinglow-frequency noise.

Patent Document 2 discloses a method in which a substantiallysimultaneously acquired image in a full pixel read-out mode and an imagein a pixel summation read-out mode are separated respectively intoluminance components and color difference components for adaptivesynthetic processing.

Patent Document 3 discloses a method in which, for a pixel to becorrected, the highest value is calculated from among pixel values of aplurality of surrounding same-color pixels having the same colorcomponent as the pixel to be corrected, and among pixel values of aplurality of surrounding different-color pixels having a color componentdifferent from that of the pixel to be corrected, the plurality ofsurrounding different-color pixels being closer to the pixel to becorrected than are the plurality of surrounding same-color pixels, and,when the pixel value of the pixel to be corrected is higher than thecalculated highest value, the pixel value of the pixel to be correctedis replaced with the calculated highest value to correct a white defect.

Patent Document 4 discloses an image processing device for eliminatingnoise from a moving image, the device comprising: a contrast calculationunit for calculating a contrast value for a target pixel in a basisimage; a motion vector calculation unit for calculating a motion vectorbetween the basis image and the reference image, the motion vectorcalculation unit using the contrast value to modify the method forcalculating the motion vector; a motion compensation unit forcompensating for motion of the reference image with respect to the basisimage on the basis of the motion vector calculated by the motion vectorcalculation unit; and a weighted addition unit for performing weightedaddition of the basis image and the reference image subjected to motioncompensation for each target pixel.

Patent Document 5 discloses an image processing device in which aninputted image and a reference image are added to eliminate noise in theinputted image.

Patent Document 6 discloses an image processing method for eliminatingnoise included in an image, the method comprising extracting ahigh-frequency component from an image, extracting a noise componentfrom the extracted high-frequency component using non-linear conversion,subtracting the extracted noise component from the image, againextracting the high-frequency component from the image from which thenoise component was subtracted, extracting a correction component usingnon-linear conversion from the high-frequency component that wasextracted again, and adding the extracted correction component to theimage from which the noise component was subtracted.

PRIOR ART DOCUMENTS Patent Documents

Patent Document 1: Japanese Patent No. 3862613

Patent Document 2: Japanese Patent Laid-open Publication No. 2008-131580

Patent Document 3: Japanese Patent Laid-open Publication No. 2011-135566

Patent Document 4: Japanese Patent Laid-open Publication No. 2012-222510

Patent Document 5: Domestic Re-publication of PCT InternationalApplication No. 2010-007777

Patent Document 6: Japanese Patent No. 4535125

SUMMARY OF INVENTION Problems to be Solved

The prior art described above presents a problem in that, if the signaland noise characteristics are not clearly separated, the effect of noiseelimination is diminished and the signal intensity may be reduced.Therefore, it is an object of the present invention to provide an imageprocessing device for eliminating noise from an image while maintainingsignal intensity, an image processing method, an image processingprogram, and a recording medium storing the program.

Means for Solving the Problems

An image processing device of the present invention that solves theproblems described above, comprises:

average image producing means for producing an average image from all orsome of a plurality of images captured at the same location;

noise extracting means for extracting a noise pixel on the basis of theresult of a comparison between the pixel values of the pixels in thecaptured images and the pixel values of the corresponding pixels in theaverage image; and

interpolating means for interpolating the pixel value of the noise pixelincluded in the captured images using the pixel values of other pixelsto produce a noise-eliminated image.

Effect of the Invention

According to the present invention, a noise pixel is extracted on thebasis of the difference in pixel values between a captured image and anaverage image. It is therefore possible to eliminate noise from an imagewhile maintaining signal intensity.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram showing the entirety of a system for acquiringa tomographic image of the fundus of an eye to be examined andprocessing the image;

FIG. 2 is an illustrative view showing a state in which a macular areaof the fundus is scanned using signal light;

FIG. 3 is an illustrative view showing a state in which a plurality oftomographic images are acquired;

FIG. 4 is a flowchart showing the procedure for a noise eliminationprocess;

FIG. 5 is a schematic view illustrating an aligning process and aprocess for extracting noise pixels;

FIG. 6 is a schematic view illustrating a noise-pixel elimination and aninterpolation process;

FIG. 7 is a flowchart showing the procedure for a noise eliminationprocess; and

FIG. 8 is a schematic view illustrating a process for generating video.

MODE OF CARRYING OUT THE INVENTION

An image processing device according to the present invention will bedescribed in detail below on the basis of embodiments and with referenceto the attached drawings. Description will be given of an example inwhich a tomographic image (one example of a captured image) of thefundus of an eye to be examined is acquired by an ophthalmologicexamination apparatus and noise is eliminated from the tomographicimage; however, the present invention can also be applied to cases inwhich other objects are captured using other types of apparatuses.

Embodiment 1

FIG. 1 is a block diagram showing the entirety of a system for acquiringa tomographic image of the fundus of an eye to be examined andprocessing the image. Reference numeral 1 indicates a fundus camera unit1 for observing and capturing an image of the fundus (retina) Ef of aneye E to be examined. The fundus camera unit 1 includes an illuminationoptical system 4, a photographic optical system 5, and a scan unit 6.

The illumination optical system 4 includes an observation light sourcesuch as a halogen lamp and a photographing light source such as a xenonlamp. The light from these light sources is guided to the fundus Ef viathe illumination optical system 4 to illuminate the fundus. Thephotographic optical system 5 includes optical elements such as anobjective lens and a photographic lens, and an imaging device such as aCCD. The photographic optical system 5 guides photographing lightreflected by the fundus Ef along a photographing optical path to theimaging device to capture an image of the fundus Ef. The photographicoptical system 5 also guides below described signal light from the OCTunit 2 to the fundus Ef and light reflected therefrom to the OCT unit 2.The scan unit 6 includes mechanisms such as galvanometer mirrors forscanning the signal light from the OCT unit 2 in the X direction and Ydirection as shown in FIG. 1.

The fundus camera unit 1 is optically connected via a connector 7 and aconnecting wire 8 to the OCT unit 2 for capturing a tomographic image ofthe fundus Ef.

The OCT unit 2 may be not only of a Fourier domain type, but also of atime domain or a swept-source type; however, the OCT unit 2 will use awell-known Fourier domain type. In this case, a low coherence lightsource 20 emits light having a wavelength of 700-1100 nm. The light fromthe low coherence light source 20 is divided into reference light andsignal light, and the reference light advances on a reference opticalpath and is reflected by a reference mirror. On the other hand, thesignal light is guided to the fundus camera unit 1 via the connectingwire 8 and the connector 7, and is scanned on the fundus Ef in the X andY directions by the scan unit 6. The signal light reflected by thefundus Ef and returned to the OCT unit 2 is superimposed on thereference light reflected by the reference mirror to produceinterference light. The interference light is analyzed in spectrum in anOCT signal detection device 21 to generate an OCT signal that indicatesinformation about the depth direction (Z direction) of the fundus.

An image processing device 3 is configured from, e.g., a microcomputerbuilt in the fundus camera unit 1, or a personal computer connected tothe fundus camera unit 1. The image processing device 3 is provided witha control unit 30 configured from CPU, RAM, ROM, and the like. Thecontrol unit 30 controls all image processing by executing an imageprocessing program.

A display unit 31 is configured from, e.g., a display device such as anLCD, and displays an image produced or processed by the image processingdevice 3 and ancillary information such as information relating to asubject.

An operation unit 32 has, e.g., a mouse, keyboard, operation panel andthe like, and is used by an operator to give commands to the imageprocessing device 3.

A tomographic image forming unit 41 is implemented by a dedicatedelectronic circuit for executing a well-known analysis method such as aFourier domain method (spectral domain method) or by the imageprocessing program executed by the CPU described above, and forms atomographic image of the fundus Ef on the basis of the OCT signaldetected by the OCT signal detection device 21. The tomographic imageformed by the tomographic image forming unit 41 is stored in a memoryunit 42 configured from, e.g., a semiconductor memory, hard disk device,or the like. The memory unit 42 also stores the image processing programdescribed above.

An image processing unit 50 performs a computation process on thetomographic image (captured image) formed by the tomographic imageforming unit 41 and eliminates noise included in the tomographic image.The image processing unit 50 is configured from aligning means 51 foraligning other captured images with a reference image, average imageproducing means 52 for producing an average image from all or some ofthe captured images, noise extracting means 53 for extracting a noisepixel on the basis of the result of a comparison between the pixelvalues of the pixels in the captured images and the pixel values of thecorresponding pixels in the average image, and interpolating means 54for interpolating the pixel value of the noise pixel with the pixelvalues of other pixels to produce a noise-eliminated image. The means orimage processes in the image processing unit 50 are implemented by useof the dedicated electronic circuit, or by executing the imageprocessing program by the control unit 30.

The operation of the image processing device 3 will be described nextwith reference to the flowchart in FIG. 4. The control unit 30 controlsthe scan unit 6 to scan the signal light on the fundus Ef at onelocation in the X-axis direction in FIG. 1. At this time, thetomographic image forming unit 41 forms one tomographic image on thebasis of the OCT signal detected by the OCT signal detection device 21.These processes are repeated N times (where N is an integer equal to orgreater than 2, e.g., N=100-300). This causes N tomographic images T_(i)(with i being 1 through N) (written as T_(i) below) of the fundus Ef atthe same location at different times t₁-t_(N) to be produced (step S1).FIG. 3 is an example of a plurality of tomographic images along scanninglines y_(j) in a region R in which a retinal macular region as shown inFIG. 2 is present. Structures constituting the fundus appear in layersin each of the tomographic images T_(i). These images are obtained byphotographing the same location (by selecting the position of the scanline y_(j) in FIG. 2); however, positional shifts may occur in theX-axis direction and Z-axis direction due to involuntary eye movementduring fixation. The thus produced tomographic images T_(i) usually havelow signal intensity and include a large amount of noise.

The aligning means 51 performs a process in which each of thetomographic images T_(i) is aligned with a reference image (step S2).Specifically, a reference image serving as an alignment reference isfirst selected or produced. The reference image may be any tomographicimage, e.g., the first tomographic image T₁, or T_(i) that is displayedon the display unit 31 and selected by an operator. Alternatively, anaverage image of the tomographic images T_(i), the tomographic imagemost similar to this average image, or an average image of a pluralityof tomographic images selected by an operator may be used as thereference image.

Next, as shown in FIG. 5, each of the tomographic images T_(i) isdivided into strip regions 60 such that each of the strip regions 60 isk pixels wide in the X direction (where, e.g., k=1). Next, local regionsare set so as to be about 20 k pixels wide in the X direction and so asto have the same length in the Z direction as the strip region 60, andthe degree of similarity relative to the corresponding local region ofthe reference image is calculated for each of the strip regions on thebasis of the set local regions to calculate the amount of shifts in theX direction and Z direction. Each of the strip regions is then moved inthe X direction and Z direction by the calculated amount of shifts,thereby performing the aligning process to produce an alignedtomographic image P_(i) as shown in the middle section of FIG. 5. InFIG. 5, the positions of the strip regions 60 of the aligned tomographicimage Pi are irregular in the Z direction (vertical direction). Thisschematically represents the amount of shifts in the Z direction.However, the amount of shift in the X direction is not shown because itis difficult to represent. The value of k can be changed in accordancewith expected noise size, image magnification, and the like. The degreeof similarity can be calculated using, e.g., formula 1 below.

$\begin{matrix}{r = \frac{\sum\limits_{k = 1}^{n}{\{ {{T_{A}(k)} - \overset{\_}{T_{A}}} \} \{ {{T_{i}(k)} - \overset{\_}{T_{i}}} \}}}{\sqrt{\sum\limits_{k = 1}^{n}\{ {{T_{A}(k)} - \overset{\_}{T_{A}}} \}^{2}}\sqrt{\sum\limits_{k = 1}^{n}\{ {{T_{i}(k)} - \overset{\_}{Ti}} \}^{2}}}} & {{Formula}\mspace{14mu} 1}\end{matrix}$

In Formula 1, T(k) represents a set of pixel values (the number ofpixels n), and T (with a horizontal line above) represents the averageof the pixel values.

Alignment can be performed by a variety of methods other than the methoddescribed above. For example, a method may be used in which alignment isperformed on the entirety of the tomographic images without dividing thetomographic images into strip regions, or a method may be used in whichparts of the tomographic images are extracted as characteristic,regions, and alignment is performed on the basis of the degree ofsimilarity of these characteristic regions. Depending on the propertiesof the photographic object, the aligning process may be omitted.

The average image producing means 52 adds together the pixel values ofthe aligned tomographic images P₁-P_(N) for each of the pixels, anddivides the resulting sum by the number of images N. This determines thepixel value of each of the pixels and produces an averaged image T_(A)(step S3). The averaged image may be produced from some of thetomographic images P_(i), rather than being produced from all of thealigned tomographic images P_(i) as described above. Alternatively, thepixel values of the averaged image may be determined using the medianvalue or the most frequently appearing value of the pixel values of thetomographic images, rather than using the arithmetic mean of the pixelvalues.

The noise extracting means 53 calculates the difference between thepixel value of each of the pixels in the aligned tomographic image P_(i)and the pixel value of the pixel in the averaged image T_(A) that islocated at the same position as the pixel in the aligned tomographicimage P_(i), and, when the absolute value of this difference is greaterthan a prescribed threshold, determines that the pixel is a noise pixel(step S4). The threshold may be incrementally varied in accordance withthe pixel values of the averaged image T_(A), rather than using a singlevalue.

The comparison between the pixel value of each of the pixels in thetomographic image T_(i) and the pixel value of the pixel in the averagedimage T_(A) that is located at the same position as the pixel in thetomographic image T_(i) may be performed using a ratio, and a pixel maybe determined to be a noise pixel when the ratio deviates from aprescribed range.

In the case of tomographic images by OCT as in the present embodiment,noise pixels may include pixels having low pixel values due to thestructure of the fundus, as indicated by the black circles (referencesymbol 61 a) in FIG. 5, and pixels having high pixel values (shot noise)due to the imaging device, as indicated by the white circles (referencesymbol 61 b) in FIG. 5. The noise extracting means 53 extracts thepixels determined to include noise for each of the tomographic imagesP_(i), as shown in the lower section of FIG. 5, and stores in the memoryunit 42 information specifying these pixels, e.g., the X and Zcoordinates of the noise pixels.

The interpolating means 54 deletes the pixels determined in step S4 toinclude noise as shown by reference symbol 62 in the upper section ofFIG. 6 (e.g., sets the pixel values thereof to 0). The pixel values ofthe deleted pixels 62 are then interpolated on the basis of, e.g., thepixel values of pixels adjacent to the deleted pixels, or the pixelvalues of pixels within a certain distance from the deleted pixels, andtomographic images Q₁-Q_(N) from which noise was eliminated (as anexample of noise-eliminated images) are produced and stored in thememory unit 42 (step S5). A variety of well-known methods other thanthat described above can be used as the method for interpolation.

The tomographic images Q₁-Q_(N) stored in the memory unit 42 from whichnoise was eliminated are displayed on the display unit 31 either one ata time or with a plurality of images lined up in a single screen imageby the control unit 30 on the basis of commands given by an operator viathe operation unit 32.

According to the image processing device 3 of the present embodiment,noise pixels are extracted on the basis of the result of a comparisonbetween the pixel values of each of the aligned tomographic images P_(i)and the averaged image T_(A), and an interpolating process is performedfor the noise pixels. It is therefore possible to eliminate noise whilemaintaining signal intensity, even when the signal intensity of thetomographic images T_(i) is low.

Because extraction of noise pixels and interpolation of noise pixels areeach performed for all of the tomographic images T_(i), a plurality of(N) distinct tomographic images from which noise was eliminated can beobtained.

Embodiment 2

A second embodiment of the present invention will be described next. Theconfiguration of the device in the second embodiment is the same as thatin the first embodiment shown in FIG. 1. The operation of the device isalso essentially the same as in the first embodiment; therefore,portions different from the first embodiment will be described withreference to the flowchart in FIG. 7 and the schematic view in FIG. 8.

The tomographic image forming unit 41 forms N tomographic imagesR₁-R_(N) of the same location on the fundus Ef of an eye E to beexamined, and the aligning means 51 aligns each of the tomographicimages R_(i). These processes are the same as in the first embodiment(steps S1 and S2). Depending on the photographed object, the aligningprocess can be omitted, the same as in the first embodiment. Noisepixels are included in the produced tomographic images R_(i), asindicated by the black circles (reference numeral 63) in FIG. 8.

The average image producing means 52 uses tomographic images having adifference in photographing time less than a prescribed thresholdrelative to the tomographic images R_(i) to produce a differentindividual average image B_(i) for the tomographic images R_(i) (stepS13). Specifically, for example, for the constant time required for asingle scan in the X direction, the individual average image B_(i) forthe tomographic images R_(i) is produced using the same method as instep S3 in FIG. 4 from the tomographic image R_(i) and M tomographicimages preceding and following same (where M is an integer equal to orgreater than 1 and less than N), i.e., from the 2M+1 tomographic imagesT_(i−M)-T_(i+M). FIG. 8 shows an example in which individual averageimages B_(i) are produced from, with M being 2, in principle fivetomographic images. The thick lines indicating the individual averageimages B_(i) show the range of tomographic images used in the productionof the individual average images B_(i).

When the number of tomographic images preceding or following atomographic image Ri is less than M as with R₁, R₂, R_(N-1) and R_(N) inFIG. 8, the average image forming means 52 forms an individual averageimage B_(i) using fewer than 2M+1 tomographic images withoutcompensating for the insufficiency. For example, because there are notomographic images preceding the tomographic image R₁, an individualaverage image is produced using only three tomographic images R₁, R₂,and R₃. This is because, rather than increasing the number oftomographic images used in the production of the individual averagedimages to improve the sharpness thereof, priority is given to avoid anincrease in photographing time difference between the tomographic imageR_(i) of interest and the last (first) tomographic image used in theproduction of an individual average image. For example, when an averagedimage for the tomographic image R₁ is produced using the tomographicimages R₁-R₅ to compensate for the insufficiency, the difference in timebetween the tomographic image R₁ and the very last tomographic image R₅may increase, and actually occurring changes in the images such as thosein the shape of a blood vessel due to pulsation may be determined to benoise and be eliminated.

The noise extracting means 53 performs a subtraction process on thepixel values in each of the tomographic images R_(i) and the individualaverage images B_(i), and extracts noise pixels using the same method asin step S4 in FIG. 4 (step S14).

The interpolating means 54 interpolates the noise pixels, producestomographic images U₁-U_(N) from which noise was eliminated, and storesthese tomographic images U₁-U_(N) in the memory unit 42. This process isthe same as that used in the first embodiment (step S5).

The control unit 30 causes the noise-eliminated tomographic imagesU₁-U_(N) from the memory unit 42 to be displayed as video on the displayunit 31 (step S6). Specifically, the tomographic images U_(i) are takenas single frames of video, and the tomographic images U₁-U_(N) aredisplayed in sequence at appropriate time intervals. Alternatively, afile in video format may be generated from the tomographic imagesU₁-U_(N) and played back.

In the present embodiment, the tomographic images U₁-U_(N) from whichnoise was eliminated are all stored in the memory unit 42, and thenvideo is displayed. However, if the processing power of the imageprocessing device 3 is great enough, it is possible to perform theseprocesses in real time. Specifically, when the time required forproducing a single tomographic image and performing the series ofprocesses on this tomographic image is shorter than the time forperforming a single scan in the X direction, the processes in stepsS2-S6 in FIG. 7 may be performed in parallel with the tomographic imagecapturing.

Also in the second embodiment, the tomographic images U_(i) from whichnoise was eliminated may be displayed on the display unit 31 as stillimages.

According to the image processing device 3 of the second embodiment, anaverage image serving as the reference for the process of extractingnoise pixels is produced for every individual tomographic image solelyfrom the tomographic images having a small photographing time differencerelative to the respective tomographic image. Therefore, it is possibleto avoid a situation in which a change such as pulsation of a bloodvessel that actually occurs in a photographed object is determined to benoise and is eliminated. Additionally, the noise-eliminated tomographicimages U_(i) are displayed as video. This allows an operator to observemovements in blood vessels, thus helping in making a diagnosis.

KEY TO THE SYMBOLS

-   -   1 Fundus camera unit    -   2 OCT unit    -   3 Image processing device    -   4 Illumination optical system    -   5 Photographic optical system    -   6 Scan unit    -   7 Connector    -   8 Connecting wire    -   20 Low coherence light source    -   21 OCT signal detection device    -   30 Control unit    -   31 Display unit    -   32 Operation unit    -   41 Tomographic image forming unit    -   42 Memory unit    -   50 Image processing unit    -   51 Aligning means    -   52 Average image producing means    -   53 Noise extracting means    -   54 Interpolating means    -   60 Strip region    -   61 a, 61 b, 63 Noise pixel    -   62 Deleted noise pixel    -   E Eye to be examined    -   Ef Fundus    -   T_(i), R_(i) Tomographic image    -   P_(i) Tomographic image after aligning process    -   Q_(i), U_(i) Tomographic image from which noise was eliminated

1. An image processing device comprising: average image producing meansfor producing an average image from all or some of a plurality of imagescaptured at the same location; noise extracting means for extracting anoise pixel on the basis of the result of a comparison between the pixelvalues of the pixels in the captured images and the pixel values of thepixels at the same position in the average image; and interpolatingmeans for interpolating the pixel value of the noise pixel included inthe captured images using the pixel values of other pixels to produce anoise-eliminated image.
 2. An image processing device according to claim1, further comprising aligning means for aligning the captured images onthe basis of a reference image selected or generated from a plurality ofthe captured images, wherein the average image producing means producesthe average image from the aligned captured images; the noise extractingmeans extracts the noise pixel on the basis of the result of acomparison between the pixel values of the pixels in the alignedcaptured images and the pixel values of the pixels at the same positionin the average image that is produced from the aligned captured images;and the interpolating means interpolates the pixel value of theextracted noise pixel using the pixel values of pixels adjacent to theextracted noise pixel to produce a noise-eliminated image.
 3. An imageprocessing device according to claim 1, wherein the noise extractingmeans calculates a difference between the pixel values of the pixels inthe captured images and the pixel values of the corresponding pixels inthe average image and extracts as a noise pixel a pixel for which theabsolute value of the difference is greater than a threshold.
 4. Animage processing device according to claim 1, wherein the average imageproducing means produces a different individual average image for eachof the captured images, and the noise extracting means extracts thenoise pixel on the basis of the result of a comparison between the pixelvalues of the pixels in the captured images and the pixel values of thecorresponding pixels in the individual average image.
 5. An imageprocessing device according to claim 4, wherein the average imageproducing means produces the individual average image from capturedimages in which the difference in photographing time in the capturedimage is less than a threshold.
 6. An image processing device accordingto claim 4, wherein the average image producing means produces theindividual average image from a captured image and a prescribed numberof other captured images closely back and forth in photographing time inthe captured image.
 7. An image processing device according to claim 1,comprising a control unit that causes the noise-eliminated images to bedisplayed as video.
 8. An image processing method comprising: producingan average image from all or some of a plurality of images captured atthe same location; extracting a noise pixel on the basis of the resultof a comparison between the pixel values of the pixels in the capturedimages and the pixel values of the pixels at the same position in theaverage image; and interpolating the pixel value of the noise pixelincluded in the captured images using the pixel values of other pixelsto produce a noise-eliminated image.
 9. An image processing programexecuted by a computer comprising: an average image producing processfor producing an average image from all or some of a plurality of imagescaptured at the same location; a noise extracting process for extractinga noise pixel on the basis of the result of a comparison between thepixel values of the pixels in the captured images and the pixel valuesof the pixels at the same position in the average image; and aninterpolating process for interpolating the pixel value of the noisepixel included in the captured images using the pixel values of otherpixels to produce a noise-eliminated image.
 10. A computer-readablerecording medium in which the image processing program of claim 9 isstored.